The best image of the US Flag appears during the human-home invasion scene in E.T. 1982. This is a classic counter juxtaposition to Close Encounters of the Third Kind, since it is a reversal of the child abduction by an A.T. (Aboriginal Terrestrial) than by an E.T.
The US flag also makes an appearance in the Elliott's classroom. Just as the themes of Close Encounters deal with psychic links, so does E.T. In this case E.T. is linked psychically to Elliott. The link becomes established when Elliott was cut, and E.T. heals him with his bioluminescent finger.
But Spielberg takes it an extra level deeper in this story about aliens, adding a synchronicity element into the mix of E.T.'s and Elliott's telepathic connection. In this case, the chaos of the classroom just happens to be synchronized to a television program that E.T. is watching at home.
The theme of love is mixed with an animal rights message, by a strange sequence of 'funny' coincidences. This is a common theme in many art house movies, but in E.T. it is weaved with humour and a charming kind of silly sitcom emotion.